Systems and methods for modulation classification of baseband signals using attention-based learned filters

ABSTRACT

Systems and methods for classifying baseband signals include receiving, at a pre-processing stage of a neural network whose objective is modulation classification performance, a complex quadrature vector of interest including a plurality of samples of a baseband signal derived from a radio frequency signal of an unknown modulation type, providing the vector of interest to a plurality of FIR filters, each of which outputs a respective intermediate filtered version of the vector of interest, combining the outputs of two or more of the FIR filters to produce a filtered version of the vector of interest, including applying respective weightings to the outputs of the FIR filters, and providing the filtered version of the vector of interest to an analysis stage of the neural network for classification with respect to a plurality of known modulation types. The neural network may apply attention-based selection to learn the filters and respective weightings.

BACKGROUND OF THE INVENTION

Radio Frequency (RF) communication systems pervade the modem world,connecting an ever-growing array of devices and services for a varietyof consumer, industrial, and defense applications. RF signal qualitydegrades in real-world communication channels through a variety ofeffects, such as multipath effects, co-channel interference, fading,transmission distance, and environmental noise. Traditionally, radiosignal classification has relied on hand-crafted, expert features and apriori knowledge about the types of radio hardware and modulationsexpected in a given environment. The proliferation of legacy and new RFcommunication standards, along with the adoption of frequency andmodulation-agile Software Defined Radio (SDR) technology, allowscommunications systems to support a broad frequency range and modulationlibrary, even on commodity level hardware. The resulting complexity inthe electromagnetic spectrum makes labor intensive analysis systemsunsustainable.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separateviews, together with the detailed description below, are incorporated inand form part of the specification, and serve to further illustrateembodiments of concepts that include the claimed invention, and explainvarious principles and advantages of those embodiments.

FIG. 1 is a block diagram illustrating selected elements of a system forclassifying baseband signals derived from radio frequency signals withrespect to modulation type, in accordance with some embodiments.

FIG. 2 is a block diagram illustrating selected elements of a neuralnetwork including pre-processing and analysis stages, in accordance withsome embodiments.

FIG. 3 is a block diagram illustrating selected elements of apre-processing stage of a neural network including a filter selectionsub-network, in accordance with some embodiments.

FIG. 4A is a block diagram illustrating selected elements of a residualstack including multiple residual units, in accordance with someembodiments.

FIG. 4B is a block diagram illustrating selected elements of a residualunit, in accordance with some embodiments.

FIG. 5 is a flow diagram of selected elements of an example method forclassifying baseband signals derived from radio frequency signals withrespect to modulation type, in accordance with some embodiments.

FIG. 6 is a flow diagram of selected elements of an example method fortraining a neural network including pre-processing and analysis stagesfor classifying baseband signals derived from radio frequency signalswith respect to modulation type, in accordance with some embodiments.

FIG. 7 is a block diagram illustrating selected elements of a modulationclassification processing unit configured for classifying basebandsignals derived from radio frequency signals with respect to modulationtype and for training a neural network including pre-processing andanalysis stages to perform such classifications, in accordance with someembodiments.

Skilled artisans will appreciate that elements in the figures areillustrated for simplicity and clarity and have not necessarily beendrawn to scale. For example, the dimensions of some of the elements inthe figures may be exaggerated relative to other elements to help toimprove understanding of embodiments of the present invention.

The apparatus and method components have been represented whereappropriate by conventional symbols in the drawings, showing only thosespecific details that are pertinent to understanding the embodiments ofthe present invention so as not to obscure the disclosure with detailsthat will be readily apparent to those of ordinary skill in the arthaving the benefit of the description herein.

DETAILED DESCRIPTION OF THE INVENTION

Disclosed herein are systems and methods for classifying basebandsignals derived from radio frequency signals with respect to modulationtype. In one embodiment, a disclosed method includes receiving, at apre-processing stage of a neural network whose objective is modulationclassification performance, a complex quadrature vector of interestincluding a plurality of samples of a baseband signal derived from aradio frequency signal of an unknown modulation type. Each sampleincludes real and imaginary parts of the baseband signal of the unknownmodulation type in the complex plane. The method also includes providingthe complex quadrature vector of interest to a first plurality of finiteimpulse response (FIR) filters, each of which transforms the complexquadrature vector of interest input into an output comprising arespective different intermediate filtered version of the complexquadrature vector of interest and combining the outputs of two or moreof the FIR filters to produce a filtered version of the complexquadrature vector of interest. The combining includes applyingrespective weightings to the outputs of the FIR filters. The method alsoincludes providing the filtered version of the complex quadrature vectorof interest to an analysis stage of the neural network forclassification with respect to a plurality of known modulation types,receiving an indication of modulation classification performance of theneural network, and modifying a filter coefficient or the respectiveweighting applied to the output of at least one FIR filter in the firstplurality of FIR filters dependent on the indication of modulationclassification performance.

In one embodiment, a disclosed system for classifying baseband signalsderived from radio frequency signals with respect to modulation typeincludes an analysis stage of a neural network whose objective ismodulation classification performance, a first plurality of finiteimpulse response (FIR) filters, and a pre-processing stage of the neuralnetwork. The pre-processing stage is configured to receive a complexquadrature vector of interest including a plurality of samples of abaseband signal derived from a radio frequency signal of an unknownmodulation type. Each sample includes real and imaginary parts of thebaseband signal of the unknown modulation type in the complex plane. Thepre-processing stage is also configured to provide the complexquadrature vector of interest to the first plurality of FIR filters,each of which transforms the complex quadrature vector of interest inputinto an output comprising a respective different intermediate filteredversion of the complex quadrature vector of interest, and to combine theoutputs of two or more of the FIR filters to produce a filtered versionof the complex quadrature vector of interest. The combining includesapplying respective weightings to the outputs of the FIR filters. Thepre-processing stage is also configured to provide the filtered versionof the complex quadrature vector of interest to the analysis stage ofthe neural network for classification with respect to a plurality ofknown modulation types, to receive an indication of modulationclassification performance of the neural network, and to modify a filtercoefficient or the respective weighting applied to the output of atleast one FIR filter in the first plurality of FIR filters dependent onthe indication of modulation classification performance.

It at least some embodiments, prior to receiving the complex quadraturevector of interest, the neural network may be trained to classifybaseband signals derived from radio frequency signals with respect tothe plurality of known modulation types.

In at least some embodiments, the training may include receiving aplurality of complex quadrature training vectors. Each training vectormay include a plurality of samples of a baseband signal derived from aradio frequency signal of a respective one of the plurality of knownmodulation types. For each of the plurality of complex quadraturetraining vectors, the training may include providing the complexquadrature training vector to the first plurality of FIR filters,providing the complex quadrature training vector to a filter selectionsub-network of the neural network, the output of which includes a filterselection vector in which each element represents a weighting to beapplied to the output of a respective one of the first plurality of FIRfilters, combining the outputs of the first plurality of FIR filters toproduce a filtered version of the complex quadrature training vector,the combining including applying the respective weightings to theoutputs of the first plurality of FIR filters, providing the filteredversion of the complex quadrature training vector to the analysis stageof the neural network, receiving, as an output of the neural network, aclassification result for the complex quadrature training vector withrespect to the plurality of known modulation types, and comparing theclassification result with the known modulation type of the basebandsignals derived from the radio frequency signal for which a plurality ofsamples is included in the complex quadrature training vector.

In some embodiments, the neural network may be trained to select thefirst plurality of FIR filters from among a second plurality of FIRfilters, the second plurality of FIR filters including the firstplurality of FIR filters and one or more additional FIR filters, and theselecting including determining respective filter coefficients for eachof the first plurality of FIR filters.

In some embodiments, the neural network may be trained to determinerespective filter coefficients for each of the first plurality of FIRfilters, the determining including applying a Lasso (L1) regularizationpenalty to bias the respective FIR filter coefficients for each of thefirst plurality of FIR filters toward zero.

In some embodiments, the neural network may be trained to determinerespective filter coefficients for each of the first plurality of FIRfilters, the determining including applying an FIR bandwidth penalty tothe objective function of the neural network to bias the respective FIRfilter coefficients for each of the first plurality of FIR filterstoward coefficients consistent with minimal bandwidth filter designs.

In some embodiments, the neural network may apply an attention-basedselection mechanism to select the two or more FIR filters from among thefirst plurality of FIR filters. In some embodiments, the neural networkmay apply an attention-based selection mechanism to determine therespective weightings represented in the filter selection vector.

In some embodiments, for a given one of the first plurality of FIRfilters, the respective weighting is zero, and the two or more FIRfilters do not include the given FIR filter. In some embodiments, therespective filter coefficients for each of the first plurality of FIRfilters may be predefined. In some embodiments, the number of FIRfilters in the first plurality of FIR filters may be predefined.

The systems and methods described herein for modulation classificationof baseband signals derived from radio frequency signals may include alearned, attention-based FIR filter data transform in a pre-processingstage for a deep learning model. The model may be trained end-to-endusing an objective function that influences FIR filter design.

An FIR filter is digital filter commonly in use in a variety ofapplication contexts. For an L order FIR filter, the output sequence isa weighted sum of the most recent input values as shown in equation (1)below. In this equation, the b_(i) terms represent filter coefficients.

$\begin{matrix}{{y\lbrack n\rbrack} = {\sum\limits_{i = 1}^{L}{b_{i} \cdot {x\lbrack {n - 1} \rbrack}}}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

Systems and methods that incorporate learned FIR filters in apre-processing stage that feeds a deep learning model for modulationdetection and classification have been shown, through simulation andexperimentation, to achieve increased modulation classificationperformance over modulation classification systems that include only adeep learning model. In some embodiments, by leveraging RFdomain-specific signal processing expertise in the objective function asit relates to FIR filter designs together with a data-driven deeplearning model, the systems described herein may achieve a 14% reductionin relative error rate over a deep-learning-only approach to modulationclassification.

FIG. 1 is a block diagram illustrating selected elements of a system 100for classifying baseband signals derived from radio frequency signalswith respect to modulation type, in accordance with some embodiments.The illustrated components of FIG. 1, along with other various modulesand components, may be coupled to each other by or through one or morecontrol or data buses that enable communication between them. The use ofcontrol and data buses for the interconnection between and exchange ofinformation among the various modules and components would be apparentto a person skilled in the art in view of the description providedherein. In various embodiments, system 100 may be, or be a component of,a base station, a mobile station, or another device configured toreceive and, in some cases, transmit baseband signals derived from radiofrequency signals, or radio frequency signals from which basebandsignals are derived, and to classify baseband signals with respect tomodulation type. In some embodiments, system 100 may be integrated withan electronic communications device, for example, a portable radio, acellular telephone, a tablet computer, and the like.

In the illustrated embodiment, system 100 includes a front end 105, atransceiver 110, an encoder/decoder 120, a modulator/demodulator 115,one or more filters 125, which may include one or more FIR filters, amodulation classification processing unit 130, which includes memory135, one or more user input mechanisms 140, and a display 145. In otherembodiments, system 100 may include more, fewer, or different elementsthan those illustrated in FIG. 1.

The front end 105 may include various digital and analog components,which for brevity are not described herein and which may be implementedin hardware, software, or a combination of both, including one or moreradio frequency filters, signal splitters, signal switches, signalcombiners, transmit power amplifiers, and the like (not shown). Thefront end 105 may include one or more wired or wireless input/output(I/O) interfaces configurable to communicate with base stations, mobilestations, or other devices configured to receive and, in some cases,transmit baseband signals derived from radio frequency signals or radiofrequency signals from which baseband signals are derived. In at leastsome embodiments, the front end 105 may receive radio frequency signalsfrom an antenna communicatively coupled to the front end 105 (notshown), optionally filter the signals using one or more radio frequencyfilters, and pass them to the transceiver 110. Likewise, the front end105 may receive radio frequency signals from the transceiver 110,optionally filter the signals using one or more radio frequency filters,and transmit them via the antenna.

In various embodiments, transceiver 110 may be or include a wirelesstransceiver such as a DMR transceiver, a P25 transceiver, a Bluetoothtransceiver, a Wi-Fi transceiver perhaps operating in accordance with anIEEE 802.11 standard, such as 802.11a, 802.11b, or 802.11g, a WiMAXtransceiver perhaps operating in accordance with an IEEE 802.16standard, an LTE transceiver, or another similar type of wirelesstransceiver configurable to communicate via a wireless radio network. Insome embodiments, transceiver 110 may be or include one or more wirelinetransceivers 110, such as an Ethernet transceiver, a Universal SerialBus (USB) transceiver, or similar transceiver configurable tocommunicate via a twisted pair wire, a coaxial cable, a fiber-optic linkor a similar physical connection to a wireline network. In variousembodiments, transceiver 110 may be or include a software definedtransceiver implemented using a frequency and modulation-agile SoftwareDefined Radio (SDR) technology. The transceiver 110 may be coupled tocombined modulator/demodulator 115, which is coupled to encoder/decoder120.

In the illustrated embodiment, the transceiver 110 receives modulatedradio frequency signals, e.g., a carrier frequency signal modulated witha baseband signal, from an antenna via the front end 105. The radiofrequency signals may be modulated using any of a variety of modulationtypes and formats, in different embodiments and at different times.Modulator/demodulator 115 extracts and demodulates the in-phase andquadrature baseband signals from the received modulated radiofrequencysignal. The transceiver 110 may communicate the demodulated basebandsignals to encoder/decoder 120, which decodes the signals to extractdata encoded in the signals. Modulator/demodulator 115 may receive abaseband signal encoded with data by encoder/decoder 120 and modulatethe baseband signal with a carrier signal to produce a modulated radiofrequency signal. The transceiver 110 transmits the modulated radiofrequency signal via the front end 105 and the antenna.

The modulation classification processing unit 130 may include amicroprocessor configured to execute program instructions that implementa neural network, including pre-processing and analysis stages, trainedfor classifying baseband signals derived from radio frequency signalswith respect to modulation type. Other program instructions, whenexecuted by the microprocessor, may perform training the neural networkfor classifying baseband signals derived from radio frequency signalswith respect to modulation type. In some embodiments, the modulationclassification processing unit 130 may include a graphics processingunit (GPU) configured to perform certain aspects of a method forclassifying baseband signals derived from radio frequency signals withrespect to modulation type or a method for training a neural network toperform such classifications. In various embodiments, memory 135 mayinclude a Read Only Memory (ROM) and a Random Access Memory (RAM) forstoring, at various times, program instructions and data for performingsome or all of the modulation classification and neural network trainingsteps set forth in FIGS. 5 and 6 and the accompanying text. In someembodiments, memory 135 may also store program instructions and data forinitializing system components, encoding and decoding voice, data,control, or other signals that may be transmitted or received betweensystem 100 and one or more base stations or mobile stations (not shown).In some embodiments, some or all of the functionality of encoder/decoder120 or of other elements of system 100 shown in FIG. 1 may beimplemented by program instructions executed by the microprocessor ofclassification processing unit 130 or another processing unit (notshown).

User input mechanisms 140 may include any of a variety of suitablemechanisms for receiving user input, such as for initializing andinitiating a modulation classification exercise or for initializing andinitiating an exercise to train a neural network for modulationclassification, as described herein. Display 145 may include anysuitable display technology for presenting information to a userincluding, for example, a modulation classification result. Each of theuser input mechanisms 140 and display 145 may be communicatively coupledto the modulation classification processing unit 130.

In at least some embodiments, one or more filters 125 may be configuredto pre-process baseband signals, or representations thereof, prior toproviding them to modulation classification processing unit 130 formodulation classification. For example, in some embodiments, filters 125may be or include an FIR filter transform module, such as FIR filtertransform module 204 illustrated in FIG. 2 and described below. In someembodiments, some or all of the functionality of FIR filter transformmodule 204 shown in FIG. 2 may be implemented by program instructionsexecuted by a microprocessor or GPU of classification processing unit130 or another processing unit (not shown).

A variety of defense and commercial applications rely on fast andaccurate signal classification. As noted above, the proliferation oflegacy and new RF communication standards, along with the adoption ofSDR technology, has led to increased complexity in the electromagneticspectrum making labor intensive analysis systems unsustainable. Thesystems and methods described herein, which incorporate FIR filters atpre-processing stage to a deep learning model for modulation detectionand classification may, in various embodiments, be used to detect andclassify RF signals of interest using limited input data, ArtificialIntelligence (AI), and Machine Learning (ML), enabling performanceimprovements over expert feature analysis methods and methods that relysolely on a deep learning model without such FIR filtering.

More specifically, the systems and methods described herein mayincorporate multiple FIR filters at a pre-processing stage for which thefilter parameters, including filter coefficients and weightings, aredetermined using a neural network with end-to-end training based onmodulation classification as the objective function. In someembodiments, the neural network may use attention-selection of thelearned filters to weight contributions of each of the filters acting ona single input to generate a single output. In some embodiments, theneural network may be trained for attention-selection of predefined FIRfilters, where the selection weights are trained but the filtercoefficients are predefined. In some embodiments, an L1 regularizationpenalty may be used to drive unneeded filter coefficients to zero. Insome embodiments, a bandwidth penalty may be applied to the objectivefunction to encourage low pass filter designs. In at least someembodiments, the techniques described herein may allow a neural networkto identify optimal filter coefficients based on training performed on alarge training set across multiple filter parameter combinations.Certain parameters of the neural networks described herein, includingconfiguration information may, in various embodiments and at differenttimes, represent initial, default, or learned parameters ofconfiguration information for neural network

In some embodiments, a neural network including the pre-processing andanalysis stages described herein may be trained to classify basebandsignals derived from radio frequency signals with respect to a pluralityof known modulation types. For example, in some embodiments, basebandsignals derived from radio frequency signals may be classified by theneural network with respect to the following twenty-four modulationtypes: BPSK, QPSK, 8PSK, 16PSK, QAM16, QAM64, 2FSK_5KHz, 2FSK_75KHz,GFSK_75KHz, GFSK_5KHz, GMSK, MSK, CPFSK_75KHz, CPFSK_5KHz, APSK16_c34,APSK32_c34, QAM32, OQPSK, PI4QPSK, FM_NB, FM_WB, AM_DSM, AM_SSM, andNOISE. In other embodiments, the neural network may be trained forclassifying baseband signals derived from radio frequency signals withrespect to more, fewer, or different known modulation types.

In some embodiments, training a neural network for classifying basebandsignals derived from radio frequency signals with respect to knownmodulation types may include adding Gaussian noise, at various levels,to degrade the signal-to-noise ratio associated with signal samplesrepresenting baseband signals of known modulation types. In someembodiments, training a neural network for classifying baseband signalsderived from radio frequency signals with respect to known modulationtypes may include corrupting signal samples representing basebandsignals of known modulation types, such as by injecting various RFchannel effects into the sample data.

In various embodiments, the systems and methods described herein may beused in an application in which the RF spectrum is surveyed to identifytransmitted signals and if, based on a baseband IQ vector of what may berelatively noisy signal samples, a modulated signal is detected, thesignal is classified with respect to multiple known modulation types.

FIG. 2 is a block diagram illustrating selected elements of a neuralnetwork 200 including pre-processing and analysis stages, in accordancewith some embodiments. In the illustrated embodiment, neural network 200receives a complex quadrature vector of interest 202 including aplurality of samples of a baseband signal derived from a radio frequencysignal of an unknown modulation type. The complex quadrature vector ofinterest 202 may be a raw or filtered IQ vector representation of thebaseband signal including 1024 samples. Each sample includes real (I)and imaginary (Q) parts of the baseband signal of the unknown modulationtype in the complex plane. In the illustrated embodiment, output 212represents a prediction of the modulation type for the baseband signalrepresented by complex quadrature vector of interest 202. For example,the output 212 of neural network 200 may be a classification resultincluding a final output vector in which each element of the finaloutput vector indicates a probability that the unknown modulation typeis a respective one of multiple known modulation types on which theneural network 200 has been trained, or on which the neural network 200is being trained.

In the illustrated example, the complex quadrature vector of interest202 is provided to a pre-processing stage including an FIR filtertransform module 204. The FIR filter transform module 204 may include aplurality of FIR filters and a filter selection sub-network forselecting two or more of the plurality of FIR filters and combiningtheir outputs as a linear weighted combination. An examplepre-processing stage including elements of an FIR filter transformmodule is illustrated in FIG. 3.

In various embodiments, a single FIR filter within the plurality of FIRfilters may be used or multiple filters cascaded or otherwise combinedto produce a filtered version of the complex quadrature vector ofinterest 202. Traditionally, matched filters are hand-engineered basedon the expected waveform of received signals. However, this approachdoes not generalize well for automatic modulation recognition given thelarge amount of waveform variation. In at least some embodiments,instead of hand-engineered custom filters for modulation classification,the systems described herein may use end-to-end training to learn thefilter coefficients and filter combinations as part of the modulationclassification task.

In at least some embodiments, the FIR filters of the FIR filtertransform module 204 may be implemented in the neural network viaconvolution. For example, the FIR filters may be implemented using aconvolutional layer that has the bias term disabled and that includes alinear activation function. In this case, the learned convolution kernelweights may correspond to the filter coefficients of the learned FIRfilters. In one example, an FIR filter transform module 204 may include16 FIR filters with 256 coefficients, which creates χ_(16,2,1024),effectively representing 16 filtered IQ vectors. In this example, theFIR filter transform module 204 may include 23,280 trainable parameters.In one embodiment, a complete module classification model, including FIRfilter transform module 204, may include 934,120 trainable parameters.

In the illustrated embodiment, an analysis stage of neural network 200includes a stack of six 2×16 residual neural network elements shown asresidual stacks 206. One example residual neural network elementsuitable for use in analysis stage of neural network 200 is illustratedin FIGS. 4A and 4B and described below. In the illustrated embodiment,the analysis stage of neural network 200 also includes a fully connectedlayer, shown as dense layer 208, that uses four scaled exponentiallinear units (SeLus), to induce self-normalizing. The output of denselayer 208 is provided to a fully connected layer, shown as SoftMax 210,that converts it into a probability distribution. The output of SoftMax210 is output 212, which represents a prediction of the modulation typefor the baseband signal represented by complex quadrature vector ofinterest 202, as described herein. In some embodiments, certaincomputations of the FIR filter transform module 204 may leverage GPUresources, if available.

In other embodiments, the analysis stage of the neural network mayinclude any number of residual neural networks, convolutional layers,pooling layers, or fully connected layers, in different combinations.

FIG. 3 is a block diagram illustrating selected elements of apre-processing stage 300 of a neural network including a filterselection sub-network, in accordance with some embodiments. Elements ofeach path of the pre-processing stage of the neural network may bereplicated to handle both the real (I) and imaginary (Q) parts of thebaseband signal. In the illustrated embodiment, pre-processing stage 300receives a complex quadrature vector input 302 including a plurality ofsamples of a baseband signal derived from a radio frequency signal of anunknown modulation type. The complex quadrature vector input 302 may bea raw or filtered IQ vector representation of the baseband signalincluding a plurality of signal samples. Each sample includes real (I)and imaginary (Q) parts of the baseband signal of the unknown modulationtype in the complex plane. In the illustrated embodiment, the output ofpre-processing stage 300 is a 1×2×1024 filtered IQ vector 308, which isprovided to the analysis stage of the neural network for modulationclassification.

In the illustrated embodiment, the raw or filtered IQ vector input 302is provided to two paths of pre-processing stage 300. More specifically,the raw or filtered IQ vector input 302 is provided to a primary path ofthe pre-processing stage and a filter selection sub-network of theprocessing stage 300. The filter selection sub-network may act as afeedback mechanism to help select the filter outputs to be combined inthe final output, and to generate the weightings for the filter outputsto be combined in the primary path to produce filtered IQ vector 308.

In the illustrated embodiment, the primary path includes a 16×1×256convolutional layer, shown as Conv2D 304, configured to implement 16constituent FIR filters with 256 coefficients, as described above inreference to FIG. 2. The outputs of the 16 constituent FIR filtersimplemented by convolutional layer 304 are provided to filtered dataselection element 306 as a 16×2×1024 set of filtered IQ data.

As illustrated in FIG. 3, an averaged Power Spectral Density (PSD)representation 310 of the raw or filtered IQ vector input 302 isgenerated on one of the paths. Generating the averaged PSDrepresentation 310 may include converting the raw or filtered IQ vectorinput into a more compressed form. More specifically, the raw orfiltered IQ vector input may be fed into a custom layer that computes anaveraged, logarithmic scale PSD representation 310 using a 128-pointFast Fourier Transform (FFT) with 120 points of overlap betweenconsecutive FFTs.

In the illustrated embodiment, the 1×128 PSD representation is fed intoa MinMaxScale element that scales the data to a [0,1] range so thatlevel shifts between different signal-to-noise levels are ignored. Theresulting scaled PSD representation 312 is then provided to the filterselection sub-network for analysis.

In at least some embodiments, the filter selection sub-network may be orinclude a small deep neural network that includes basic convolutional,pooling, and dense layers. In the illustrated embodiment, the filterselection sub-network includes a 16×1×8 convolutional layer shown asConv2D 314, a 1×2 pooling layer shown as MaxPool 316, a 16×1×4convolutional layer shown as Conv2D 318, a second 1×2 pooling layershown as MaxPool 320, two fully connected layers that use a scaledexponential linear unit (SeLu), shown as dense layers 322 and 324, toinduce self-normalizing, and a fully connected layer, shown as SoftMax326, that converts the output of dense layer 324 into a probabilitydistribution.

In the illustrated embodiment, the output of this sub-network is an Nelement softmax vector representing a filter selection vector, eachelement of which represents a respective weighting for one of the Nselected FIR filters. This softmax vector may function as an attentionmechanism, allowing the model to select the most relevant filters on aper vector basis. The filtered data, χ_(16,2,1024), and the filterselection vector are then combined in a custom layer, shown as filtereddata selection element 306, that computes the filtered IQ vector 308from a weighted sum of the intermediate filtered vectors output by theselected FIR filters according to equation (2) below.

$\begin{matrix}{{{{for}\mspace{14mu} n} \in \lbrack {0,1023} \rbrack},{{i \in {\lbrack {0,1} \rbrack{y_{i}\lbrack n\rbrack}}} = {\sum\limits_{k = 1}^{N}{w_{k} \cdot {x_{ik}\lbrack n\rbrack}}}}} & {{Equation}\mspace{14mu}(2)}\end{matrix}$

In Equation (2) above, N represents the number of selected FIR filterswhose outputs are to be combined, x_(ik) represents an output of thek^(th) one of the selected FIR filters, and w_(k) represents theweighting to be applied to the k^(th) one of the FIR filters. Asillustrated in FIG. 3, in at least some embodiments, the filtered IQvector 308 may be restored to the original 1×2×1024 shape of the complexquadrature vector input 302 prior to being passed on to the analysisstage of the neural network for modulation classification. In at leastsome embodiments, the use of softmax activation, which isdifferentiable, rather than a filter selector that returns an indicationof a maximum value, facilitates end-to-end training, and provides moreflexible filtering combinations without creating greater than unityfilter gain.

In some embodiments, training the neural network may include applying anattention-based selection mechanism to select the N FIR filters whoseoutputs are to be combined from among the FIR filters included in an FIRfilter bank. In at least some embodiments, the neural network may betrained to select the plurality of FIR filters in the FIR filter bankfrom among a larger collection of possible FIR filters. Selecting theFIR filters to be included in the FIR filter bank may includedetermining respective filter coefficients for each of the FIR filtersin the FIR filter bank.

In some embodiments, the neural network may be trained to determinerespective filter coefficients for each of the FIR filters in the FIRfilter bank. in some embodiments, determining the filter coefficientsmay include applying a Lasso (L1) regularization penalty to bias therespective FIR filter coefficients for each of the FIR filters in theFIR filter bank toward zero. In some embodiments, determining the filtercoefficients may include applying an FIR bandwidth penalty to theobjective function of the neural network to bias the respective FIRfilter coefficients for each of the FIR filters in the FIR filter banktoward coefficients consistent with minimal bandwidth filter designs.

In at least some embodiments, the neural networks described herein maylearn that the inclusion of a given one of the FIR filters in the set ofselected FIR filters does not significantly improve the modulationclassification result. In this case, the learned weighting for the givenFIR filter may be extremely low compared to the learned weightings forother FIR filters or may be zero. In some embodiments, FIR filters whoselearned weighting is zero or a non-zero number below a predefinedthreshold may be excluded from contributing to the filtered IQ vector308 output by the pre-processing stage 300.

FIG. 4A is a block diagram illustrating selected elements of a residualstack 400 including multiple residual units, in accordance with someembodiments. In the illustrated embodiment, residual stack 400 includesa 32×1×1 linear convolutional layer shown as Conv2D 402, two 32×2×16residual units, shown as residual units 404 and 406, and a 1×2 poolinglayer shown as MaxPool 408. Unlike in some existing modulationclassification systems that use a (2,3) kernel within the residualunits, the systems described herein may use a (2,16) kernel in theresidual units. In at least some embodiments, the increased kernel sizemay significantly increase the number of model parameters and trainingtime but may yield markedly improved performance over systems that use a(2,3) kernel.

FIG. 4B is a block diagram illustrating selected elements of a residualunit 410 in accordance with some embodiments. In various embodiments,one or both of residual unit 404 and residual unit 406 illustrated inFIG. 4A may be similar to residual unit 410. In the illustratedembodiment, residual unit 410 includes a 32×2×16 convolutional layershown as Conv2D 412, a 32×2×16 linear convolutional layer shown asConv2D 414, and a summing element 416.

Referring now to FIG. 5, there is provided a flow diagram of selectedelements of an example method 500 for classifying baseband signalsderived from radio frequency signals with respect to modulation type, inaccordance with some embodiments. While a particular order of operationsis indicated in FIG. 5 for illustrative purposes, the timing andordering of such operations may vary where appropriate without negatingthe purpose and advantages of the examples set forth in detailthroughout the remainder of this disclosure. In various embodiments,some or all of the operations of method 500 may be performed by amodulation classification processing unit within a base station, amobile station, or another device configured to receive and, in somecases, transmit baseband signals, such as modulation classificationprocessing unit 130 illustrated in FIG. 1 or modulation classificationprocessing unit 700 illustrated in FIG. 7.

In this example embodiment, method 500 begins with block 502 andcontinues with block 504, where a neural network includingpre-processing and analysis stages is trained for classifying basebandsignals derived from radio frequency signals with respect to knownmodulation types. The objective function for the neural network ismodulation classification performance. One example method for trainingthe neural network is illustrated in FIG. 6 and described below.

At 506, method 500 includes receiving, at the pre-processing stage, acomplex quadrature vector of interest including a plurality of samplesof a baseband signal derived from a radio frequency signal of an unknownmodulation type. Each sample includes real (I) and imaginary (Q) partsof the baseband signal of the unknown modulation type in the complexplane. In at least some embodiments, the pre-processing stage mayinclude a filter selection sub-network, as described herein.

At 508, the method includes, at the pre-processing stage, providing thecomplex quadrature vector of interest to a plurality of FIR filters,each of which outputs a respective intermediate filtered version of thecomplex quadrature vector of interest. In some embodiments, one or bothof the number of filters and the filter coefficients may be predefined.In some embodiments, one or both of the number of filters and the filtercoefficients may be learned by the neural network during training andmay be refined while in use to classify baseband signals.

At 510, method 500 includes, at the pre-processing stage, combining theoutputs of two or more of the FIR filters to produce a filtered versionof the complex quadrature vector of interest. Combining the FIR filteroutputs includes applying respective weightings to the FIR filteroutputs. For example, the filtered version of the complex quadraturevector of interest may represent a linear weighted combination of therespective intermediate filtered versions of the vector of interestoutput by the two or more FIR filters. In some embodiments, therespective weightings may be learned by the neural network and the twoor more FIR filters may include some or all of the FIR filters for whichthe respective weighting is non-zero or exceeds a predetermined minimumthreshold.

At 512, the method includes providing the filtered version of thecomplex quadrature vector of interest to the analysis stage of theneural network for classification with respect to known modulationtypes. In various embodiments, the analysis stage of the neural networkmay include one or more of a residual neural network, a convolutionallayer, a pooling layer, and a fully connected layer, in differentcombinations.

At 514, the method includes receiving, an indication of modulationclassification performance of the neural network.

At 516, method 500 includes modifying a filter coefficient or theweighting applied to the output of at least one FIR filter dependent onthe indication of modulation classification performance.

In at least some embodiments, some or all of the operations of method500 illustrated in FIG. 5 may be repeated one or more times to classifysubsequently received baseband signals derived from radio frequencysignals with respect to modulation type in a neural network thatincludes pre-processing and analysis stages.

Referring now to FIG. 6, there is provided a flow diagram of selectedelements of an example method 600 for training a neural networkincluding pre-processing and analysis stages for classifying basebandsignals derived from radio frequency signals with respect to modulationtype, in accordance with some embodiments. While a particular order ofoperations is indicated in FIG. 6 for illustrative purposes, the timingand ordering of such operations may vary where appropriate withoutnegating the purpose and advantages of the examples set forth in detailthroughout the remainder of this disclosure. In various embodiments,some or all of the operations of method 600 may be performed by amodulation classification processing unit within a base station, amobile station, or another device configured to receive and, in somecases, transmit baseband signals, such as modulation classificationprocessing unit 130 illustrated in FIG. 1 or modulation classificationprocessing unit 700 illustrated in FIG. 7.

In this example embodiment, method 600 begins with block 602 andcontinues with block 604, where a plurality of complex quadraturetraining vectors is received at a neural network that includespre-processing and analysis stages and whose objective is modulationclassification performance. Each of the complex quadrature trainingvectors may include a plurality of samples of a baseband signal derivedfrom a radio frequency signal of a respective known modulation type onwhich the neural network is to be trained. For example, in someembodiments, the known modulation types on which the neural network isto be trained may include any of all of the following: BPSK, QPSK, 8PSK,16PSK, QAM16, QAM64, 2FSK_5KHz, 2FSK_75KHz, GFSK_75KHz, GFSK_5KHz, GMSK,MSK, CPFSK_75KHz, CPFSK_5KHz, APSK16_c34, APSK32_c34, QAM32, OQPSK,PI4QPSK, FM_NB, FM_WB, AM_DSM, and AM_SSM. In some embodiments, inaddition to the known modulation types, the neural network may also betrained to classify a baseband signal derived from a radio frequencysignal with respect to noise. Each signal sample may include real (I)and imaginary (Q) parts of the baseband signal of the known modulationtype in the complex plane. In some embodiments, training the neuralnetwork for classifying baseband signals derived from radio frequencysignals with respect to modulation type may include adding Gaussiannoise, at various levels, to the samples to degrade the signal-to-noiseratio. In some embodiments, the complex quadrature training vectors usedin the training may be corrupted by introducing other real-world RFchannel effects into some or all of the samples.

At 606, method 600 optionally includes, selecting a predefined pluralityof FIR filters and respective filter coefficients. In other embodiments,a plurality of FIR filters and respective filter coefficients may belearned by the neural network during the training.

At 608, the method includes providing a given training vector to theplurality of filters. At 610, method 600 includes providing the giventraining vector to a filter selection sub-network as input forgenerating a filter selection vector, each element of which represents aweighting for a respective FIR filter output. In some embodiments, thenumber of elements in the filter selection vector corresponds to thenumber of FIR filters in the plurality of filters. In some embodiments,the number of elements in the filter selection vector corresponds to atarget or maximum number of FIR filters whose outputs are to be combinedto produce a filtered version of the given training vector.

At 612, the method includes combining the outputs of two or more of theFIR filters, including applying their respective weightings, to producea filtered version of the given training vector. In some embodiments,the number of FIR filters whose outputs are to be combined to produce afiltered version of the given training vector may be learned. In someembodiments, the neural network may be constrained to select, as the twoor more FIR filters whose outputs are to be combined, no more than thenumber of FIR filters for which a corresponding element exists in thefilter selection vector.

In some embodiments, the neural network may be trained to select theplurality of FIR filters from among a larger collection of FIR filters,with the selecting including determining respective filter coefficientsfor each of the plurality of FIR filters. In some embodiments, thetraining may include applying an attention-based selection mechanism toselect the two or more FIR filters whose outputs are to be combined fromamong the plurality of FIR filters. In some embodiments, the neuralnetwork may be trained to determine respective filter coefficients foreach of the plurality of FIR filters, the determining including applyinga Lasso (L1) regularization penalty to bias the respective FIR filtercoefficients for each of the plurality of FIR filters toward zero. Insome embodiments, training the neural network to determine respectivefilter coefficients for each of the plurality of FIR filters may includeapplying an FIR bandwidth penalty to the objective function of theneural network to bias the respective FIR filter coefficients for eachof the plurality of FIR filters toward coefficients consistent withminimal bandwidth filter designs.

In some embodiments, the training may include applying anattention-based selection mechanism to determine the respectiveweightings represented in the filter selection vector. In someembodiments, the two or more FIR filters whose outputs are combined mayinclude some or all of the FIR filters for which the respectiveweighting is non-zero or exceeds a predetermined minimum threshold. Thetechniques described herein for combining multiple FIR filters togenerate a filtered version of a complex quadrature vector may, invarious embodiments and at different times, result in the selection of asingle FIR filter in a bank of FIR filters, a cascade of FIR filters inthe bank of FIR filters, or a linear weighted combination of any numberof the FIR filters in the FIR filter bank. The neural networks describedherein may learn which combinations of FIR filters, along with theirrespective coefficients and weightings, lead to the best overallmodulation classification performance in a particular applicationcontext or for a wide variety of application contexts.

At 614, method 600 includes providing the filtered version of the giventraining vector to an analysis stage of the neural network and receivinga modulation classification result. In various embodiments, the analysisstage of the neural network may include one or more of a residual neuralnetwork, a convolutional layer, a pooling layer, and a fully connectedlayer, in different combinations. The classification result for thebaseband signal derived from the radio frequency signal of the unknownmodulation type may include a final output vector in which each elementof the final output vector indicates a probability that the unknownmodulation type is a respective one of the known modulation types.

At 616, the method includes comparing the classification result for thegiven training vector to the known modulation type of the correspondingbaseband signal to determine modulation classification performance forthe neural network.

At 618, method 600 includes modifying a configuration parameter, filtercoefficient, or filter output weighting for the neural network based onthe classification performance. In various embodiments, modifying aconfiguration parameter may include, for example, modifying a constrainton the number of FIR filters whose outputs are combined to generate thefiltered version of the training vectors, or changing the number, type,or configuration of neural network layers or other elements included inthe neural network to improve modulation classification performance.

If, at 620, there are additional complex quadrature training vectors tobe considered, method 600 may return to 608, after which the operationsshown as 608 through 618 may be repeated for each additional complexquadrature training vector. Otherwise, the training exercise may becomplete, as shown at 622.

In at least some embodiments, some or all of the operations of method600 illustrated in FIG. 6 may be repeated one or more times to train,retrain, or improve the modulation classification performance of theneural network as additional complex quadrature training vectors forbaseband signals of the same or different known modulation types becomeavailable or in response to determining that the modulationclassification performance does not yet meet a desired performancetarget.

In various embodiments, the techniques described herein for classifyingbaseband signals derived from radio frequency signals with respect tomodulation type or for training a neural network including thepre-processing and analysis stages described herein to perform suchclassifications may be implemented by a modulation classificationprocessing unit of a base station or a mobile station. In otherembodiments, these techniques may be implemented by a modulationclassification processing unit of another type of device, outside of thecontext of a base station or mobile station, that is configured toreceive and classify baseband signals derived from radio frequencysignals or to receive radio frequency signals from which basebandsignals can be derived and those baseband signals subsequentlyclassified.

FIG. 7 is a block diagram illustrating selected elements of a modulationclassification processing unit 700 configured for classifying basebandsignals derived from radio frequency signals with respect to modulationtype and for training a neural network that includes pre-processing andanalysis stages to perform such classifications, in accordance with someembodiments. In some embodiments, modulation classification processingunit 700 may be similar to modulation classification processing unit 130illustrated in FIG. 1. In the illustrated example, modulationclassification processing unit 700 includes a Read Only Memory (ROM)710, a Random Access Memory (RAM) 720, an electronic processor 730, oneor more input/output device interfaces 740 for communicating withlocally attached devices and components, and a network interface 750 forcommunicating with a remote server or device (not shown in FIG. 7), allof which are coupled to a system bus 705 through which they communicatewith each other. In various embodiments, the electronic processor 730may include a microprocessor, a graphics processing unit, amicrocontroller, a system-on-chip, a field-programmable gate array, aprogrammable mixed-signal array, or, in general, any system orsub-system that includes nominal memory and that is capable of executinga sequence of instructions in order to control hardware.

In the illustrated embodiment, ROM 710 stores program instructions 715,at least some of which may be executed by the electronic processor 730to perform the methods described herein. Modulation classificationprocessing unit 700 may thus be configured to implement a neural networkincluding a pre-processing stage and an analysis stage, as describedherein, for generating a modulation classification result. In someembodiments, modulation classification processing unit 700 may beconfigured to implement training a neural network including apre-processing stage and an analysis stage for generating a modulationclassification result. In some embodiments, modulation classificationprocessing unit 700 may also be configured to implement a filteringstage of the neural network. In one example, program instructions 715may be executed on electronic processor 730 to implement a convolutionallayer that effectively implements 16 constituent FIR filters with 256coefficients, as described herein. In other embodiments, a filteringstage for the neural network may be implemented by filters outside ofmodulation classification processing unit 700, such as with filters 125shown in FIG. 1. In various embodiments, any or all of the operations ofmethod 400 illustrated in FIG. 4 or method 500 illustrated in FIG. 5 maybe performed by program instructions 715 executing on electronicprocessor 730 of modulation classification processing unit 700.

For example, program instructions 715 may, when executed by electronicprocessor 730, be operable to receive, at a pre-processing stage of aneural network whose objective is modulation classification performance,a complex quadrature vector of interest including a plurality of samplesof a baseband signal derived from a radio frequency signal of an unknownmodulation type, to provide the vector of interest to a plurality of FIRfilters, each of which transforms the vector of interest input into anoutput comprising a respective different intermediate filtered versionof the vector of interest, to combine the outputs of two or more of theFIR filters to produce a filtered version of the vector of interest,including applying respective weightings to the outputs of the FIRfilters, to provide the filtered version of the vector of interest to ananalysis stage of the neural network for classification with respect toa plurality of known modulation types, to receive an indication ofmodulation classification performance of the neural network, and tomodify a filter coefficient or the respective weighting applied to theoutput of at least one FIR filter in the plurality of FIR filtersdependent on the indication of modulation classification performance.

In another example, program instructions 715 may, when executed byelectronic processor 730, be operable to receive a plurality of complexquadrature training vectors, each training vector including a pluralityof samples of a baseband signal derived from a radio frequency signal ofa respective one of the plurality of known modulation types and, foreach of the plurality of training vectors, to provide the trainingvector to a plurality of FIR filters, to provide the training vector toa filter selection sub-network of the neural network, the output ofwhich includes a filter selection vector in which each elementrepresents a weighting to be applied to the output of a respective oneof the FIR filters, to combine the outputs of the FIR filters to producea filtered version of the training vector, including applying therespective weightings to the outputs of the FIR filters, to provide thefiltered version of the training vector to the analysis stage of theneural network, to receive, as an output of the neural network, aclassification result for the training vector with respect to theplurality of known modulation types, and to compare the classificationresult with the known modulation type of the baseband signals derivedfrom the radio frequency signal for which a plurality of samples isincluded in the complex quadrature training vector.

In some embodiments, program instructions 715 may be stored in anothertype of non-volatile memory, such as a hard disk, a CD-ROM, an opticalstorage device, a magnetic storage device, a PROM (Programmable ReadOnly Memory), an EPROM (Erasable Programmable Read Only Memory), anEEPROM (Electrically Erasable Programmable Read Only Memory) or a Flashmemory. In some embodiments, program instructions 715 may includeprogram instructions that when executed by electronic processor 730implement other functionality features of a base station, mobilestation, or other device configured to receive and, in some cases,transmit baseband signals derived from radio frequency signals or radiofrequency signals from which baseband signals are derived, in additionto program instructions that, when executed, cause the electronicprocessor 730 to classify baseband signals with respect to modulationtype or to train a neural network to perform such classifications. Forexample, in some embodiments, program instructions 715 may, whenexecuted by electronic processor 730, be operable to perform encodingsignals to be transmitted or decoding received signals.

In this example embodiment, RAM 720 may, from time to time, storeprogram data 725 including, without limitation, configurationinformation for a neural network that includes the pre-processing andanalysis stages described herein. In various embodiments, theconfiguration information may include information indicating a number ofFIR filters for which the outputs are to be combined to produce afiltered version of a complex quadrature vector in a classification orneural network training exercise, a combination of filter coefficientsfor the FIR filters to be used in a classification or neural networktraining exercise, respective weightings to be applied to outputs of theFIR filters to be used in a classification or neural network trainingexercise, the number, type, or configuration of neural network layers orother elements included the neural network, or other data accessible byprogram instruction 715 and used in performing the methods describedherein. Certain elements of this program data may, in variousembodiments and at different times, represent initial, default, orlearned configuration information for the neural network.

In some embodiments, RAM 720 may also store data used in performingother functions of the modulation classification processing unit 700. Insome embodiments, RAM 720 may, from time to time, store local copies ofall or a portion of program instructions 715 or other programinstructions copied from ROM 710 or received over network interface 750.

In this example embodiment, input/output device interfaces 740 mayinclude one or more analog input interfaces, such as one or moreanalog-to-digital (A/D) convertors, or digital interfaces for receivingsignals or data from, and sending signals or data to, one or moreinput/output devices. In some embodiments, may include one or moreanalog input interfaces for receiving baseband or radio frequencysignals. In some embodiments, input/output device interfaces 740 mayinclude one or more external memory interfaces through which modulationclassification processing unit 700 may be coupled to an external memory(not shown in FIG. 7). Such an external memory may include, for example,a hard-disk drive (HDD), an optical disk drive such as a compact disk(CD) drive or digital versatile disk (DVD) drive, a solid-state drive(SSD), a tape drive, a flash memory drive, or a tape drive, to name afew. In various embodiments, or at certain times, some or all of programdata 725 may reside in external memory rather than, or in addition to,within RAM 720.

In various embodiments, input/output device interfaces 740 may operateto receive user input, to provide system output, or a combination ofboth. User input may be provided via, for example, a keyboard or keypad,a microphone, soft keys, icons, or soft buttons on a touch screen of adisplay, such as display 145 illustrated in FIG. 1, a scroll ball, amouse, buttons, and the like. Input/output device interfaces 740 mayalso include other input mechanisms, which for brevity are not describedherein and which may be implemented in hardware, software, or acombination of both. In some embodiments, input/output device interfaces740 may include a graphical user interface (GUI) generated, for example,by electronic processor 730 from program instructions 715 and programdata 725 and presented on display 145, enabling a user to interact withdisplay 145.

Network interface 750 may be a suitable system, apparatus, or deviceoperable to serve as an interface between electronic processor 730 and anetwork. Network interface 750 may enable modulation classificationprocessing unit 700 to communicate over a network using a suitabletransmission protocol or standard, including, but not limited to,transmission protocols and standards enumerated below with respect tothe discussion of the network. In some embodiments, network interface750 may be communicatively coupled via a network to a network storageresource. The network may be implemented as, or may be a part of, astorage area network (SAN), personal area network (PAN), local areanetwork (LAN), a metropolitan area network (MAN), a wide area network(WAN), a wireless local area network (WLAN), a virtual private network(VPN), an intranet, the Internet or another appropriate architecture orsystem that facilitates the communication of signals, data or messages,which are generally referred to as data. The network may transmit datausing a desired storage or communication protocol, including, but notlimited to, Fibre Channel, Frame Relay, Asynchronous Transfer Mode(ATM), Internet protocol (IP), other packet-based protocol, smallcomputer system interface (SCSI), Internet SCSI (iSCSI), Serial AttachedSCSI (SAS) or another transport that operates with the SCSI protocol,advanced technology attachment (ATA), serial ATA (SATA), advancedtechnology attachment packet interface (ATAPI), serial storagearchitecture (SSA), integrated drive electronics (IDE), or anycombination thereof. The network and its various components may beimplemented using hardware, software, or any combination thereof.

Network interface 750 may enable wired or wireless communications to andfrom modulation classification processing unit 700 and other elements ofa base station, mobile station, or other device configured to receiveand classify baseband signals derived from radio frequency signals or toreceive radio frequency signals from which baseband signals can bederived and those baseband signals subsequently classified. In someembodiments, baseband or radio frequency signals may also oralternatively be received over network interface 750 rather than one ofinput/output device interfaces 740.

The systems and methods described herein for classifying basebandsignals derived from radio frequency signals with respect to modulationtype may employ end-to-end training of learned filters usingclassification performance as an objective function. In someembodiments, an L1 regularization penalty may be used to drive unneededfilter coefficients to zero. In some embodiments, a bandwidth penaltymay be applied to the objective function to encourage low pass filterdesigns. In some embodiments, these systems and methods may useattention-selection of learned filters to determine the contributions,and corresponding output weightings, of each learned FIR filter.

In experiments to evaluate the techniques described herein, three modelswere evaluated to demonstrate the performance improvement of thetechnique. In a baseline model, the FIR filter transform module wasremoved entirely. In a predefined model, the FIR filter transform modulewas used, but the FIR filter weightings were fixed based on a set ofpredefined FIR filter coefficients. For example, the filter coefficientsof the predefined model were chosen to provide various bandpassbandwidths, flat passbands, and high noise rejection outside thepassband. In a learned model, the FIR filter coefficients were learnedas part of the end-to-end modulation classification model training. Morespecifically, the use of the FIR filter transform modules describedherein for pre-processing complex quadrature vector data prior toproviding the complex quadrature vector data to an analysis stage of aneural network was shown to result in a 14% reduction in relative errorrate in modulation classification compared to a traditional deeplearning model with such pre-processing.

The FIR filter frequency responses from the best learned model exhibitedmuch wider variety in filter behavior than did the basic bandpassfilters provided in the predefined case. The predefined filters werebroadly selected, with concentrations on two of the narrower filters.However, the learned filters were heavily weighted to a subset of theavailable filters that corresponded to the most mature, well-definedfrequency responses. While perhaps not as ‘sharp’ as hand-generatedexpert filters they nonetheless exhibited many traditional filtercharacteristics and appeared to be settling on various common matchedfilter variations. These results indicate that the number of learned FIRfilters may be reduced with minimal performance impact.

While the experiments described above were used to compare modulationclassification performance between predefined and learned filterscenarios, in some embodiments of the neural networks described herein,these two approaches may be applied in parallel. For example, in onehybrid approach, two FIR filter banks, one predefined and one learned,may be used with the same attention mechanism. In another hybridapproach, a learned model may begin with a rough set of expertly craftedfilter coefficients, such as those used in the predefined modeldescribed above, and end-to-end training may be applied to evolve thefilter design from this starting point, rather than from a uniformfilter starting point or from scratch.

In the foregoing specification, specific embodiments have beendescribed. However, one of ordinary skill in the art appreciates thatvarious modifications and changes can be made without departing from thescope of the invention as set forth in the claims below. Accordingly,the specification and figures are to be regarded in an illustrativerather than a restrictive sense, and all such modifications are intendedto be included within the scope of present teachings.

The benefits, advantages, solutions to problems, and any element(s) thatmay cause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeatures or elements of any or all the claims. The invention is definedsolely by the appended claims including any amendments made during thependency of this application and all equivalents of those claims asissued.

Moreover, in this document, relational terms such as first and second,top and bottom, and the like may be used solely to distinguish oneentity or action from another entity or action without necessarilyrequiring or implying any actual such relationship or order between suchentities or actions. The terms “comprises,” “comprising,” “has”,“having,” “includes”, “including,” “contains”, “containing” or any othervariation thereof, are intended to cover a non-exclusive inclusion, suchthat a process, method, article, or apparatus that comprises, has,includes, contains a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus. An element proceeded by“comprises . . . a”, “has . . . a”, “includes . . . a”, “contains . . .a” does not, without more constraints, preclude the existence ofadditional identical elements in the process, method, article, orapparatus that comprises, has, includes, contains the element. The terms“a” and “an” are defined as one or more unless explicitly statedotherwise herein. The terms “substantially”, “essentially”,“approximately”, “about” or any other version thereof, are defined asbeing close to as understood by one of ordinary skill in the art, and inone non-limiting embodiment the term is defined to be within 10%, inanother embodiment within 5%, in another embodiment within 1% and inanother embodiment within 0.5%. The term “coupled” as used herein isdefined as connected, although not necessarily directly and notnecessarily mechanically. A device or structure that is “configured” ina certain way is configured in at least that way, but may also beconfigured in ways that are not listed.

It will be appreciated that some embodiments may be comprised of one ormore generic or specialized processors, or “processing devices”, such asmicroprocessors, digital signal processors, GPUs, customized processorsand field programmable gate arrays (FPGAs) and unique stored programinstructions, including both software and firmware, that control the oneor more processors to implement, in conjunction with certainnon-processor circuits, some, most, or all of the functions of themethod or apparatus described herein. Alternatively, some or allfunctions could be implemented by a state machine that has no storedprogram instructions, or in one or more application specific integratedcircuits (ASICs), in which each function or some combinations of certainof the functions are implemented as custom logic. Of course, acombination of the two approaches could be used.

Moreover, an embodiment can be implemented as a computer-readablestorage medium having computer readable code stored thereon forprogramming a computer including for example, a processor, to perform amethod as described and claimed herein. Examples of suchcomputer-readable storage mediums include, but are not limited to, ahard disk, a CD-ROM, an optical storage device, a magnetic storagedevice, a ROM (Read Only Memory), a PROM (Programmable Read OnlyMemory), an EPROM (Erasable Programmable Read Only Memory), an EEPROM(Electrically Erasable Programmable Read Only Memory) and a Flashmemory. Further, it is expected that one of ordinary skill,notwithstanding possibly significant effort and many design choicesmotivated by, for example, available time, current technology, andeconomic considerations, when guided by the concepts and principlesdisclosed herein will be readily capable of generating such softwareinstructions and programs and ICs with minimal experimentation.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter lies in less than allfeatures of a single disclosed embodiment. Thus, the following claimsare hereby incorporated into the Detailed Description, with each claimstanding on its own as a separately claimed subject matter.

We claim:
 1. A method for classifying baseband signals derived fromradio frequency signals with respect to modulation type, comprising:receiving, at a pre-processing stage of a neural network whose objectiveis modulation classification performance, a complex quadrature vector ofinterest including a plurality of samples of a baseband signal derivedfrom a radio frequency signal of an unknown modulation type, each sampleincluding real and imaginary parts of the baseband signal of the unknownmodulation type in the complex plane; providing the complex quadraturevector of interest to a first plurality of finite impulse response (FIR)filters, each of which transforms the complex quadrature vector ofinterest input into an output comprising a respective differentintermediate filtered version of the complex quadrature vector ofinterest; combining the outputs of two or more of the first plurality ofFIR filters to produce a filtered version of the complex quadraturevector of interest, the combining including applying respectiveweightings to the outputs of the two or more FIR filters; providing thefiltered version of the complex quadrature vector of interest to ananalysis stage of the neural network for classification with respect toa plurality of known modulation types; receiving an indication ofmodulation classification performance of the neural network; andmodifying a filter coefficient or the respective weighting applied tothe output of at least one FIR filter in the first plurality of FIRfilters dependent on the indication of modulation classificationperformance.
 2. The method of claim 1, further comprising, prior toreceiving the complex quadrature vector of interest, training the neuralnetwork to classify baseband signals derived from radio frequencysignals with respect to the plurality of known modulation types.
 3. Themethod of claim 2, further comprising training the neural network toselect the first plurality of FIR filters from among a second pluralityof FIR filters, the second plurality of FIR filters including the firstplurality of FIR filters and one or more additional FIR filters, and theselecting including determining respective filter coefficients for eachof the first plurality of FIR filters.
 4. The method of claim 2, whereintraining the neural network further comprises applying anattention-based selection mechanism to select the two or more FIRfilters from among the first plurality of FIR filters.
 5. The method ofclaim 2, further comprising training the neural network to determinerespective filter coefficients for each of the first plurality of FIRfilters, the determining including applying a Lasso (L1) regularizationpenalty to bias the respective FIR filter coefficients for each of thefirst plurality of FIR filters toward zero.
 6. The method of claim 2,further comprising training the neural network to determine respectivefilter coefficients for each of the first plurality of FIR filters, thedetermining including applying an FIR bandwidth penalty to the objectivefunction of the neural network to bias the respective FIR filtercoefficients for each of the first plurality of FIR filters towardcoefficients consistent with minimal bandwidth filter designs.
 7. Themethod of claim 1, further comprising, prior to receiving the complexquadrature vector of interest, training the neural network to classifybaseband signals derived from radio frequency signals with respect tothe plurality of known modulation types, the training including:receiving a plurality of complex quadrature training vectors, eachtraining vector including a plurality of samples of a baseband signalderived from a radio frequency signal of a respective one of theplurality of known modulation types; for each of the plurality ofcomplex quadrature training vectors: providing the complex quadraturetraining vector to the first plurality of FIR filters; providing thecomplex quadrature training vector to a filter selection sub-network ofthe neural network, the output of which includes a filter selectionvector in which each element represents a weighting to be applied to theoutput of a respective one of the first plurality of FIR filters;combining the outputs of the first plurality of FIR filters to produce afiltered version of the complex quadrature training vector, thecombining including applying the respective weightings to the outputs ofthe first plurality of FIR filters; providing the filtered version ofthe complex quadrature training vector to the analysis stage of theneural network; receiving, as an output of the neural network, aclassification result for the complex quadrature training vector withrespect to the plurality of known modulation types; and comparing theclassification result with the known modulation type of the basebandsignals derived from the radio frequency signal for which a plurality ofsamples is included in the complex quadrature training vector.
 8. Themethod of claim 7, wherein training the neural network further comprisesapplying an attention-based selection mechanism to determine therespective weightings represented in the filter selection vector.
 9. Themethod of claim 7, wherein: for a given one of the first plurality ofFIR filters, the respective weighting is zero; and the two or more FIRfilters do not include the given FIR filter.
 10. The method of claim 1,wherein respective filter coefficients for each of the first pluralityof FIR filters are predefined.
 11. The method of claim 1, wherein thenumber of FIR filters in the first plurality of FIR filters ispredefined.
 12. A system for classifying baseband signals derived fromradio frequency signals with respect to modulation type, comprising: ananalysis stage of a neural network whose objective is modulationclassification performance; a first plurality of finite impulse response(FIR) filters; and a pre-processing stage of the neural networkconfigured to: receive a complex quadrature vector of interest includinga plurality of samples of a baseband signal derived from a radiofrequency signal of an unknown modulation type, each sample includingreal and imaginary parts of the baseband signal of the unknownmodulation type in the complex plane; provide the complex quadraturevector of interest to the first plurality of FIR filters, each of whichtransforms the complex quadrature vector of interest input into anoutput comprising a respective different intermediate filtered versionof the complex quadrature vector of interest; combine the outputs of twoor more of the first plurality of FIR filters to produce a filteredversion of the complex quadrature vector of interest, the combiningincluding applying respective weightings to the outputs of the two ormore FIR filters; provide the filtered version of the complex quadraturevector of interest to the analysis stage of the neural network forclassification with respect to a plurality of known modulation types;receive an indication of modulation classification performance of theneural network; and modify a filter coefficient or the respectiveweighting applied to the output of at least one FIR filter in the firstplurality of FIR filters dependent on the indication of modulationclassification performance.
 13. The system of claim 12, furthercomprising a filter selection sub-network of the neural networkconfigured to output a filter selection vector in which each elementrepresents a weighting to be applied to the output of a respective oneof the first plurality of FIR filters; wherein, prior to receiving thecomplex quadrature vector of interest, the pre-processing stage of theneural network is configured to: receive a plurality of complexquadrature training vectors, each training vector including a pluralityof samples of a baseband signal derived from a radio frequency signal ofa respective one of the plurality of known modulation types; and foreach of the plurality of complex quadrature training vectors: providethe complex quadrature training vector to the first plurality of FIRfilters; provide the complex quadrature training vector to the filterselection sub-network as an input to generation of the filter selectionvector; combine the outputs of the first plurality of FIR filters toproduce a filtered version of the complex quadrature training vector,the combining including applying the respective weightings in the filterselection vector to the outputs of the first plurality of FIR filters;and provide the filtered version of the complex quadrature trainingvector to the analysis stage of the neural network; and wherein, foreach of the plurality of complex quadrature training vectors, theanalysis stage of the neural network is configured to: generate aclassification result for the complex quadrature training vector withrespect to the plurality of known modulation types; and compare theclassification result with the known modulation type of the basebandsignals derived from the radio frequency signal for which a plurality ofsamples is included in the complex quadrature training vector.
 14. Thesystem of claim 13, further comprising a second plurality of FIR filtersincluding the first plurality of FIR filters and one or more additionalFIR filters, wherein the filter selection sub-network of the neuralnetwork is further configured to select the first plurality of FIRfilters from among the second plurality of FIR filters, the selectingincluding determining respective filter coefficients for each of thefirst plurality of FIR filters.
 15. The system of claim 13, wherein thefilter selection sub-network of the neural network is further configuredto determine respective filter coefficients for each of the firstplurality of FIR filters, the determining including applying a Lasso(L1) regularization penalty to bias the respective FIR filtercoefficients for each of the first plurality of FIR filters toward zero.16. The system of claim 13, wherein the filter selection sub-network ofthe neural network is further configured to determine respective filtercoefficients for each of the first plurality of FIR filters, thedetermining including applying an FIR bandwidth penalty to the objectivefunction of the neural network to bias the respective FIR filtercoefficients for each of the first plurality of FIR filters towardcoefficients consistent with minimal bandwidth filter designs.
 17. Thesystem of claim 13, wherein the filter selection sub-network of theneural network is further configured to apply an attention-basedselection mechanism to select the two or more FIR filters from among thefirst plurality of FIR filters.
 18. The system of claim 13, wherein thefilter selection sub-network of the neural network is further configuredto apply an attention-based selection mechanism to determine therespective weightings represented in the filter selection vector. 19.The system of claim 13, wherein: for a given one of the first pluralityof FIR filters, the respective weighting is zero; and the two or moreFIR filters do not include the given FIR filter.
 20. The system of claim13, wherein at least one of respective filter coefficients for each ofthe first plurality of FIR filters and the number of FIR filters in thefirst plurality of FIR filters is predefined.